Luc Blanchet

Abstract

The article reviews the current status of a theoretical approach to the problem of the emissionof gravitational waves by isolated systems in the context of general relativity. Part A of thearticle deals with general post-Newtonian sources. The exterior field of the source is investigatedby means of a combination of analytic post-Minkowskian and multipolar approximations. Thephysical observables in the far-zone of the source are described by a specific set of radiativemultipole moments. By matching the exterior solution to the metric of the post-Newtoniansource in the near-zone we obtain the explicit expressions of the source multipole moments.The relationships between the radiative and source moments involve many non-linear multipoleinteractions, among them those associated with the tails (and tails-of-tails) of gravitationalwaves. Part B of the article is devoted to the application to compact binary systems. We presentthe equations of binary motion, and the associated Lagrangian and Hamiltonian, at the thirdpost-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energyflux, taking consistently into account the relativistic corrections in the binary moments as well asthe various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism.The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing thesignals from inspiralling compact binaries, is deduced from an energy balance argument.